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Confused .... y=x-|x|

by mikebc
Tags: confused, yx|x|
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mikebc
#1
Feb19-08, 11:08 AM
P: 20
The problem is to graph this equation y=x-|x|.



From what I understand of absolute values, this x would be positive. If it is positive then y=0 and there would be no points to graph. Is there something that I am missing? The question is worth 4 points, so I can't see the answer just being 0. Thanks for any suggestions.
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#2
Feb19-08, 11:16 AM
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P: 15,066
What happens when x is negative?
dranseth
#3
Feb19-08, 11:22 AM
P: 89
What I was taught to do when dealing with absolute value, is to rewrite the equation so that the absolute value is isolated, then find the 2 equations.

so you'll have:
x=x-y
y=o

and also:
x=-x+y
2x=y

mikebc
#4
Feb19-08, 11:47 AM
P: 20
Confused .... y=x-|x|

The absolute value of -x would be x. But I remember with inequalities there are 2 possible answers with absolute value (-,+). From what you are explaining it sounds like that is what you are saying to do, use both possible values. Then I would graph by beginning with y at 0 and continue by substituting values into 2x=y? That seems to make sense to me. Thank you both for your help!
K.J.Healey
#5
Feb19-08, 11:53 AM
P: 641
Also just try plugging in some numbers:
For 2 -> Y = 2 - |2| = 0
For -2 - > Y = -2 -|-2| = -2 -2 = -4
see?
So for negatives you have Y = 2X, X<0
symbolipoint
#6
Feb19-08, 01:33 PM
HW Helper
PF Gold
P: 2,797
Solve or graph y = x - |x|.

If x>0, then y = x - x, meaning y=0.

If x<0, then y = x - (-x) [ notice those are parentheses, not absolute value notation symbols ], meaning y = x + x = 2x.
HallsofIvy
#7
Feb19-08, 02:15 PM
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Thanks
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P: 39,345
Quote Quote by mikebc View Post
The problem is to graph this equation y=x-|x|.



From what I understand of absolute values, this x would be positive.
Surely you didn't mean to say that! x itself can be any number. |x| is always positive (or 0- don't forget that!

Quote Quote by dranseth View Post
What I was taught to do when dealing with absolute value, is to rewrite the equation so that the absolute value is isolated, then find the 2 equations.

so you'll have:
x=x-y
y=o
Why did you switch to x=? If x[itex]\ge 0[/itex] y= x- x= 0. The graph is just the x axis from x= 0 to the right.

and also:
x=-x+y
2x=y
If x< 0, don't forget that. Then y= x- (-x)= 2x.

Quote Quote by mikebc View Post
The absolute value of -x would be x.
No, no, no! |-x|= |x| which may be eigther x or -x depending upon what x is.

But I remember with inequalities there are 2 possible answers with absolute value (-,+). From what you are explaining it sounds like that is what you are saying to do, use both possible values. Then I would graph by beginning with y at 0 and continue by substituting values into 2x=y? That seems to make sense to me. Thank you both for your help!
Draw the graph of y= 2x, to the left of x= 0. To the right, the graph is just y= 0, the x-axis.
dranseth
#8
Feb19-08, 05:04 PM
P: 89
I rearranged the formula to isolate the absolute value.
mikebc
#9
Feb19-08, 06:59 PM
P: 20
Wow, you guys couldn't have made it any more clear for me. Thanks alot!


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